Question

Vijay weighed $65\frac{1}{2}kg$. He gained $1\frac{2}{5}kg$ during the first week, $1\frac{1}{4}kg$ during the second week, but lost $\frac{5}{16}kg$ during the third week. What was his weight after the third week?

Answer 1

Step 1: Convert the given statement into a mathematical equation
The weight gain should be added to his original weight and the weight loss should be subtracted from it.
So,
Final weight =$65\frac{1}{2}+1\frac{2}{5}+1\frac{1}{4}-\frac{5}{16}$

=$\frac{65\times 2+1}{2}+\frac{1\times 5+2}{5}+\frac{1\times 4+1}{4}-\frac{5}{16}$

=$\frac{130+1}{2}+\frac{5+2}{5}+\frac{4+1}{4}-\frac{5}{16}$

=$\frac{131}{2}+\frac{7}{5}+\frac{5}{4}-\frac{5}{16}$

Step 2: Convert the fractions into like fraction and find the final weight of Vijay

$\frac{131}{2}+\frac{7}{5}+\frac{5}{4}-\frac{5}{16}$

=$\frac{131\times 40+7\times 16+5\times 20-5\times 5}{80}$

=$\frac{5240+112+100-25}{80}$

= $\frac{5427}{80}$kg

Hence, Vijay's weight after the third week is $\frac{5427}{80}$ or $67\frac{67}{80}$ kg